. An octagon has a side length of 15 feet and an area of 1089.6 ft?. Find the area of a smaller octagon that has a side length of 7 feet.

Question

An octagon has a side length of 15 feet and an area of 1089.6 ft²

Find the area of a smaller octagon that has a side length of 7 feet.

237.3ft²

Step-by-step explanation:

We are given two octagons in the above question.

Side length of larger octagon = 15 ft

Area of larger octagon = 1089.6 ft²

The area of a smaller octagon = X

Side length of smaller octagon = 7 ft.

We solve for this using scale factor

Scale factor(k) = ratio of the side length of the octagon = smaller side length/ larger side length

k = 7/15

It is important to note that

The square of the scale factor k = ratio of the areas of the octagon

Hence,

k² = X/1089.6 ft²

(7/15)² = X/1089.6 ft²

7²/15² = X/1089.6 ft²

Cross Multiply

15² × X = 7² × 1089.6ft²

X = 7² × 1089.6ft²/15²

X = 237.29066667ft²

Approximately, the area of the smaller octagon = 237.3ft²

q1 a person or thing situated away or detached from the main body or system. a cluster is a a mash of many things.

q2 do

step-by-step explanation:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.